LMFDB - Embedded newform 990.2.k.c.287.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(287,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.287"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,0,0,0,0,0,-12,0,0,-12,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 32x^{9} + 9x^{8} - 16x^{7} + 464x^{6} - 80x^{5} + 225x^{4} - 4000x^{3} + 15625 $ x^12 - 32x^9 + 9x^8 - 16x^7 + 464x^6 - 80x^5 + 225x^4 - 4000*x^3 + 15625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			287.4
Root			$-1.46707 - 1.68751i$ of defining polynomial
Character	$\chi$	$=$	990.287
Dual form			990.2.k.c.683.4

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.68751 + 1.46707i) q^{5} +(-0.220441 - 0.220441i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.155875 + 2.23063i) q^{10} -1.00000i q^{11} +(3.56880 - 3.56880i) q^{13} -0.311751 q^{14} -1.00000 q^{16} +(1.29519 - 1.29519i) q^{17} -1.64906i q^{19} +(1.46707 + 1.68751i) q^{20} +(-0.707107 - 0.707107i) q^{22} +(-2.90643 - 2.90643i) q^{23} +(0.695400 - 4.95141i) q^{25} -5.04704i q^{26} +(-0.220441 + 0.220441i) q^{28} +3.24589 q^{29} +5.81287 q^{31} +(-0.707107 + 0.707107i) q^{32} -1.83168i q^{34} +(0.695400 + 0.0485942i) q^{35} +(-7.26705 - 7.26705i) q^{37} +(-1.16606 - 1.16606i) q^{38} +(2.23063 + 0.155875i) q^{40} -4.97333i q^{41} +(6.32247 - 6.32247i) q^{43} -1.00000 q^{44} -4.11032 q^{46} +(-3.53601 + 3.53601i) q^{47} -6.90281i q^{49} +(-3.00945 - 3.99289i) q^{50} +(-3.56880 - 3.56880i) q^{52} +(6.03331 + 6.03331i) q^{53} +(1.46707 + 1.68751i) q^{55} +0.311751i q^{56} +(2.29519 - 2.29519i) q^{58} -6.33213 q^{59} -1.69396 q^{61} +(4.11032 - 4.11032i) q^{62} +1.00000i q^{64} +(-0.786709 + 11.2581i) q^{65} +(2.68599 + 2.68599i) q^{67} +(-1.29519 - 1.29519i) q^{68} +(0.526083 - 0.457360i) q^{70} +0.733819i q^{71} +(2.84498 - 2.84498i) q^{73} -10.2772 q^{74} -1.64906 q^{76} +(-0.220441 + 0.220441i) q^{77} +13.9310i q^{79} +(1.68751 - 1.46707i) q^{80} +(-3.51668 - 3.51668i) q^{82} +(3.45193 + 3.45193i) q^{83} +(-0.285514 + 4.08580i) q^{85} -8.94133i q^{86} +(-0.707107 + 0.707107i) q^{88} -14.0326 q^{89} -1.57342 q^{91} +(-2.90643 + 2.90643i) q^{92} +5.00067i q^{94} +(2.41929 + 2.78281i) q^{95} +(4.93128 + 4.93128i) q^{97} +(-4.88102 - 4.88102i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{13} - 12 q^{16} - 8 q^{17} + 8 q^{23} - 16 q^{31} - 4 q^{37} + 8 q^{38} + 4 q^{40} + 8 q^{43} - 12 q^{44} + 16 q^{46} + 24 q^{47} + 8 q^{50} + 12 q^{52} - 16 q^{53} + 4 q^{58} - 32 q^{59} + 16 q^{61}+ \cdots + 24 q^{98}+O(q^{100}) $ 12 * q - 12 * q^13 - 12 * q^16 - 8 * q^17 + 8 * q^23 - 16 * q^31 - 4 * q^37 + 8 * q^38 + 4 * q^40 + 8 * q^43 - 12 * q^44 + 16 * q^46 + 24 * q^47 + 8 * q^50 + 12 * q^52 - 16 * q^53 + 4 * q^58 - 32 * q^59 + 16 * q^61 - 16 * q^62 - 8 * q^67 + 8 * q^68 + 8 * q^70 + 20 * q^73 - 32 * q^74 - 12 * q^82 - 40 * q^85 + 8 * q^92 + 16 * q^95 + 36 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−1.68751	+	1.46707i	−0.754679	+	0.656095i
$5$	−1.68751	+	1.46707i	−0.754679	+	0.656095i
$6$		0			0
$7$	−0.220441	−	0.220441i	−0.0833188	−	0.0833188i	0.664219	−	0.747538i	$-0.268764\pi$
$7$	−0.220441	−	0.220441i	−0.0833188	−	0.0833188i	−0.747538	+	0.664219i	$0.768764\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−0.155875	+	2.23063i	−0.0492921	+	0.705387i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$		0			0
$13$	3.56880	−	3.56880i	0.989807	−	0.989807i	−0.0101420	−	0.999949i	$-0.503228\pi$
$13$	3.56880	−	3.56880i	0.989807	−	0.989807i	0.999949	+	0.0101420i	$0.00322834\pi$
$14$	−0.311751			−0.0833188
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.29519	−	1.29519i	0.314131	−	0.314131i	−0.532377	−	0.846507i	$-0.678701\pi$
$17$	1.29519	−	1.29519i	0.314131	−	0.314131i	0.846507	+	0.532377i	$0.178701\pi$
$18$		0			0
$19$		−	1.64906i		−	0.378321i	−0.981946	−	0.189160i	$-0.939423\pi$
$19$		−	1.64906i		−	0.378321i	0.981946	−	0.189160i	$-0.0605766\pi$
$20$	1.46707	+	1.68751i	0.328047	+	0.377339i
$21$		0			0
$22$	−0.707107	−	0.707107i	−0.150756	−	0.150756i
$23$	−2.90643	−	2.90643i	−0.606033	−	0.606033i	0.335874	−	0.941907i	$-0.390968\pi$
$23$	−2.90643	−	2.90643i	−0.606033	−	0.606033i	−0.941907	+	0.335874i	$0.890968\pi$
$24$		0			0
$25$	0.695400	−	4.95141i	0.139080	−	0.990281i
$26$		−	5.04704i		−	0.989807i
$27$		0			0
$28$	−0.220441	+	0.220441i	−0.0416594	+	0.0416594i
$29$	3.24589			0.602747			0.301374	−	0.953506i	$-0.402555\pi$
$29$	3.24589			0.602747			0.301374	+	0.953506i	$0.402555\pi$
$30$		0			0
$31$	5.81287			1.04402			0.522011	−	0.852939i	$-0.325182\pi$
$31$	5.81287			1.04402			0.522011	+	0.852939i	$0.325182\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	1.83168i		−	0.314131i
$35$	0.695400	+	0.0485942i	0.117544	+	0.00821392i
$36$		0			0
$37$	−7.26705	−	7.26705i	−1.19470	−	1.19470i	−0.975733	−	0.218963i	$-0.929733\pi$
$37$	−7.26705	−	7.26705i	−1.19470	−	1.19470i	−0.218963	−	0.975733i	$-0.570267\pi$
$38$	−1.16606	−	1.16606i	−0.189160	−	0.189160i
$39$		0			0
$40$	2.23063	+	0.155875i	0.352693	+	0.0246460i
$41$		−	4.97333i		−	0.776704i	−0.921511	−	0.388352i	$-0.873044\pi$
$41$		−	4.97333i		−	0.776704i	0.921511	−	0.388352i	$-0.126956\pi$
$42$		0			0
$43$	6.32247	−	6.32247i	0.964168	−	0.964168i	−0.0352119	−	0.999380i	$-0.511211\pi$
$43$	6.32247	−	6.32247i	0.964168	−	0.964168i	0.999380	+	0.0352119i	$0.0112106\pi$
$44$	−1.00000			−0.150756
$45$		0			0
$46$	−4.11032			−0.606033
$47$	−3.53601	+	3.53601i	−0.515780	+	0.515780i	−0.916292	−	0.400512i	$-0.868832\pi$
$47$	−3.53601	+	3.53601i	−0.515780	+	0.515780i	0.400512	+	0.916292i	$0.368832\pi$
$48$		0			0
$49$		−	6.90281i		−	0.986116i
$50$	−3.00945	−	3.99289i	−0.425601	−	0.564681i
$51$		0			0
$52$	−3.56880	−	3.56880i	−0.494903	−	0.494903i
$53$	6.03331	+	6.03331i	0.828739	+	0.828739i	0.987342	−	0.158604i	$-0.0506992\pi$
$53$	6.03331	+	6.03331i	0.828739	+	0.828739i	−0.158604	+	0.987342i	$0.550699\pi$
$54$		0			0
$55$	1.46707	+	1.68751i	0.197820	+	0.227544i
$56$			0.311751i			0.0416594i
$57$		0			0
$58$	2.29519	−	2.29519i	0.301374	−	0.301374i
$59$	−6.33213			−0.824373			−0.412186	−	0.911100i	$-0.635235\pi$
$59$	−6.33213			−0.824373			−0.412186	+	0.911100i	$0.635235\pi$
$60$		0			0
$61$	−1.69396			−0.216889			−0.108445	−	0.994102i	$-0.534587\pi$
$61$	−1.69396			−0.216889			−0.108445	+	0.994102i	$0.534587\pi$
$62$	4.11032	−	4.11032i	0.522011	−	0.522011i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−0.786709	+	11.2581i	−0.0975793	+	1.39639i
$66$		0			0
$67$	2.68599	+	2.68599i	0.328146	+	0.328146i	0.851881	−	0.523735i	$-0.175462\pi$
$67$	2.68599	+	2.68599i	0.328146	+	0.328146i	−0.523735	+	0.851881i	$0.675462\pi$
$68$	−1.29519	−	1.29519i	−0.157065	−	0.157065i
$69$		0			0
$70$	0.526083	−	0.457360i	0.0628789	−	0.0546650i
$71$			0.733819i			0.0870884i	0.999052	+	0.0435442i	$0.0138649\pi$
$71$			0.733819i			0.0870884i	−0.999052	+	0.0435442i	$0.986135\pi$
$72$		0			0
$73$	2.84498	−	2.84498i	0.332980	−	0.332980i	−0.520737	−	0.853717i	$-0.674343\pi$
$73$	2.84498	−	2.84498i	0.332980	−	0.332980i	0.853717	+	0.520737i	$0.174343\pi$
$74$	−10.2772			−1.19470
$75$		0			0
$76$	−1.64906			−0.189160
$77$	−0.220441	+	0.220441i	−0.0251216	+	0.0251216i
$78$		0			0
$79$			13.9310i			1.56736i	0.621166	+	0.783679i	$0.286659\pi$
$79$			13.9310i			1.56736i	−0.621166	+	0.783679i	$0.713341\pi$
$80$	1.68751	−	1.46707i	0.188670	−	0.164024i
$81$		0			0
$82$	−3.51668	−	3.51668i	−0.388352	−	0.388352i
$83$	3.45193	+	3.45193i	0.378898	+	0.378898i	0.870705	−	0.491806i	$-0.163663\pi$
$83$	3.45193	+	3.45193i	0.378898	+	0.378898i	−0.491806	+	0.870705i	$0.663663\pi$
$84$		0			0
$85$	−0.285514	+	4.08580i	−0.0309683	+	0.443167i
$86$		−	8.94133i		−	0.964168i
$87$		0			0
$88$	−0.707107	+	0.707107i	−0.0753778	+	0.0753778i
$89$	−14.0326			−1.48745			−0.743724	−	0.668487i	$-0.766942\pi$
$89$	−14.0326			−1.48745			−0.743724	+	0.668487i	$0.766942\pi$
$90$		0			0
$91$	−1.57342			−0.164939
$92$	−2.90643	+	2.90643i	−0.303017	+	0.303017i
$93$		0			0
$94$			5.00067i			0.515780i
$95$	2.41929	+	2.78281i	0.248214	+	0.285511i
$96$		0			0
$97$	4.93128	+	4.93128i	0.500695	+	0.500695i	0.911654	−	0.410959i	$-0.134806\pi$
$97$	4.93128	+	4.93128i	0.500695	+	0.500695i	−0.410959	+	0.911654i	$0.634806\pi$
$98$	−4.88102	−	4.88102i	−0.493058	−	0.493058i
$99$		0			0
$100$	−4.95141	−	0.695400i	−0.495141	−	0.0695400i
$101$		−	7.22294i		−	0.718709i	−0.933201	−	0.359355i	$-0.882997\pi$
$101$		−	7.22294i		−	0.718709i	0.933201	−	0.359355i	$-0.117003\pi$
$102$		0			0
$103$	13.0883	−	13.0883i	1.28962	−	1.28962i	0.354609	−	0.935015i	$-0.384614\pi$
$103$	13.0883	−	13.0883i	1.28962	−	1.28962i	0.935015	−	0.354609i	$-0.115386\pi$
$104$	−5.04704			−0.494903
$105$		0			0
$106$	8.53239			0.828739
$107$	−6.08443	+	6.08443i	−0.588204	+	0.588204i	−0.937145	−	0.348941i	$-0.886542\pi$
$107$	−6.08443	+	6.08443i	−0.588204	+	0.588204i	0.348941	+	0.937145i	$0.386542\pi$
$108$		0			0
$109$			15.4240i			1.47735i	0.674060	+	0.738677i	$0.264549\pi$
$109$			15.4240i			1.47735i	−0.674060	+	0.738677i	$0.735451\pi$
$110$	2.23063	+	0.155875i	0.212682	+	0.0148621i
$111$		0			0
$112$	0.220441	+	0.220441i	0.0208297	+	0.0208297i
$113$	1.01545	+	1.01545i	0.0955254	+	0.0955254i	0.753255	−	0.657729i	$-0.228483\pi$
$113$	1.01545	+	1.01545i	0.0955254	+	0.0955254i	−0.657729	+	0.753255i	$0.728483\pi$
$114$		0			0
$115$	9.16859	+	0.640697i	0.854976	+	0.0597453i
$116$		−	3.24589i		−	0.301374i
$117$		0			0
$118$	−4.47749	+	4.47749i	−0.412186	+	0.412186i
$119$	−0.571027			−0.0523460
$120$		0			0
$121$	−1.00000			−0.0909091
$122$	−1.19781	+	1.19781i	−0.108445	+	0.108445i
$123$		0			0
$124$		−	5.81287i		−	0.522011i
$125$	6.09057	+	9.37576i	0.544757	+	0.838594i
$126$		0			0
$127$	−2.31919	−	2.31919i	−0.205795	−	0.205795i	0.596682	−	0.802477i	$-0.296485\pi$
$127$	−2.31919	−	2.31919i	−0.205795	−	0.205795i	−0.802477	+	0.596682i	$0.796485\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	7.40438	+	8.51695i	0.649407	+	0.746986i
$131$		−	2.58260i		−	0.225642i	−0.993615	−	0.112821i	$-0.964011\pi$
$131$		−	2.58260i		−	0.225642i	0.993615	−	0.112821i	$-0.0359887\pi$
$132$		0			0
$133$	−0.363521	+	0.363521i	−0.0315212	+	0.0315212i
$134$	3.79857			0.328146
$135$		0			0
$136$	−1.83168			−0.157065
$137$	−2.39766	+	2.39766i	−0.204846	+	0.204846i	−0.802072	−	0.597227i	$-0.796269\pi$
$137$	−2.39766	+	2.39766i	−0.204846	+	0.204846i	0.597227	+	0.802072i	$0.296269\pi$
$138$		0			0
$139$			15.3059i			1.29823i	0.760690	+	0.649115i	$0.224861\pi$
$139$			15.3059i			1.29823i	−0.760690	+	0.649115i	$0.775139\pi$
$140$	0.0485942	−	0.695400i	0.00410696	−	0.0587720i
$141$		0			0
$142$	0.518889	+	0.518889i	0.0435442	+	0.0435442i
$143$	−3.56880	−	3.56880i	−0.298438	−	0.298438i
$144$		0			0
$145$	−5.47749	+	4.76196i	−0.454881	+	0.395459i
$146$		−	4.02341i		−	0.332980i
$147$		0			0
$148$	−7.26705	+	7.26705i	−0.597348	+	0.597348i
$149$	8.11299			0.664642			0.332321	−	0.943166i	$-0.392168\pi$
$149$	8.11299			0.664642			0.332321	+	0.943166i	$0.392168\pi$
$150$		0			0
$151$	−8.68914			−0.707112			−0.353556	−	0.935413i	$-0.615028\pi$
$151$	−8.68914			−0.707112			−0.353556	+	0.935413i	$0.615028\pi$
$152$	−1.16606	+	1.16606i	−0.0945802	+	0.0945802i
$153$		0			0
$154$			0.311751i			0.0251216i
$155$	−9.80929	+	8.52790i	−0.787901	+	0.684977i
$156$		0			0
$157$	−11.5457	−	11.5457i	−0.921446	−	0.921446i	0.0756854	−	0.997132i	$-0.475886\pi$
$157$	−11.5457	−	11.5457i	−0.921446	−	0.921446i	−0.997132	+	0.0756854i	$0.975886\pi$
$158$	9.85069	+	9.85069i	0.783679	+	0.783679i
$159$		0			0
$160$	0.155875	−	2.23063i	0.0123230	−	0.176347i
$161$			1.28139i			0.100988i
$162$		0			0
$163$	−8.19627	+	8.19627i	−0.641981	+	0.641981i	−0.951042	−	0.309061i	$-0.899985\pi$
$163$	−8.19627	+	8.19627i	−0.641981	+	0.641981i	0.309061	+	0.951042i	$0.399985\pi$
$164$	−4.97333			−0.388352
$165$		0			0
$166$	4.88176			0.378898
$167$	15.2871	−	15.2871i	1.18295	−	1.18295i	0.203976	−	0.978976i	$-0.434614\pi$
$167$	15.2871	−	15.2871i	1.18295	−	1.18295i	0.978976	−	0.203976i	$-0.0653863\pi$
$168$		0			0
$169$		−	12.4726i		−	0.959434i
$170$	2.68721	+	3.09099i	0.206099	+	0.237068i
$171$		0			0
$172$	−6.32247	−	6.32247i	−0.482084	−	0.482084i
$173$	−0.320800	−	0.320800i	−0.0243900	−	0.0243900i	0.694807	−	0.719197i	$-0.255490\pi$
$173$	−0.320800	−	0.320800i	−0.0243900	−	0.0243900i	−0.719197	+	0.694807i	$0.755490\pi$
$174$		0			0
$175$	−1.24479	+	0.938198i	−0.0940970	+	0.0709211i
$176$			1.00000i			0.0753778i
$177$		0			0
$178$	−9.92251	+	9.92251i	−0.743724	+	0.743724i
$179$	11.8322			0.884382			0.442191	−	0.896921i	$-0.354201\pi$
$179$	11.8322			0.884382			0.442191	+	0.896921i	$0.354201\pi$
$180$		0			0
$181$	2.85138			0.211942			0.105971	−	0.994369i	$-0.466205\pi$
$181$	2.85138			0.211942			0.105971	+	0.994369i	$0.466205\pi$
$182$	−1.11257	+	1.11257i	−0.0824695	+	0.0824695i
$183$		0			0
$184$			4.11032i			0.303017i
$185$	22.9245	+	1.60196i	1.68545	+	0.117778i
$186$		0			0
$187$	−1.29519	−	1.29519i	−0.0947140	−	0.0947140i
$188$	3.53601	+	3.53601i	0.257890	+	0.257890i
$189$		0			0
$190$	3.67844	+	0.257048i	0.266862	+	0.0186482i
$191$			24.5026i			1.77294i	0.462784	+	0.886471i	$0.346851\pi$
$191$			24.5026i			1.77294i	−0.462784	+	0.886471i	$0.653149\pi$
$192$		0			0
$193$	10.0278	−	10.0278i	0.721820	−	0.721820i	−0.247156	−	0.968976i	$-0.579496\pi$
$193$	10.0278	−	10.0278i	0.721820	−	0.721820i	0.968976	+	0.247156i	$0.0794960\pi$
$194$	6.97388			0.500695
$195$		0			0
$196$	−6.90281			−0.493058
$197$	15.1983	−	15.1983i	1.08283	−	1.08283i	0.0865874	−	0.996244i	$-0.472404\pi$
$197$	15.1983	−	15.1983i	1.08283	−	1.08283i	0.996244	−	0.0865874i	$-0.0275962\pi$
$198$		0			0
$199$			24.7030i			1.75115i	0.483085	+	0.875574i	$0.339516\pi$
$199$			24.7030i			1.75115i	−0.483085	+	0.875574i	$0.660484\pi$
$200$	−3.99289	+	3.00945i	−0.282340	+	0.212800i
$201$		0			0
$202$	−5.10739	−	5.10739i	−0.359355	−	0.359355i
$203$	−0.715528	−	0.715528i	−0.0502202	−	0.0502202i
$204$		0			0
$205$	7.29624	+	8.39256i	0.509591	+	0.586162i
$206$		−	18.5096i		−	1.28962i
$207$		0			0
$208$	−3.56880	+	3.56880i	−0.247452	+	0.247452i
$209$	−1.64906			−0.114068
$210$		0			0
$211$	4.53147			0.311960			0.155980	−	0.987760i	$-0.450147\pi$
$211$	4.53147			0.311960			0.155980	+	0.987760i	$0.450147\pi$
$212$	6.03331	−	6.03331i	0.414369	−	0.414369i
$213$		0			0
$214$			8.60469i			0.588204i
$215$	−1.39373	+	19.9448i	−0.0950517	+	1.36022i
$216$		0			0
$217$	−1.28139	−	1.28139i	−0.0869867	−	0.0869867i
$218$	10.9064	+	10.9064i	0.738677	+	0.738677i
$219$		0			0
$220$	1.68751	−	1.46707i	0.113772	−	0.0989100i
$221$		−	9.24457i		−	0.621857i
$222$		0			0
$223$	−0.652316	+	0.652316i	−0.0436823	+	0.0436823i	−0.728611	−	0.684928i	$-0.759834\pi$
$223$	−0.652316	+	0.652316i	−0.0436823	+	0.0436823i	0.684928	+	0.728611i	$0.259834\pi$
$224$	0.311751			0.0208297
$225$		0			0
$226$	1.43606			0.0955254
$227$	2.09545	−	2.09545i	0.139080	−	0.139080i	−0.634139	−	0.773219i	$-0.718645\pi$
$227$	2.09545	−	2.09545i	0.139080	−	0.139080i	0.773219	+	0.634139i	$0.218645\pi$
$228$		0			0
$229$		−	5.36435i		−	0.354486i	−0.984167	−	0.177243i	$-0.943282\pi$
$229$		−	5.36435i		−	0.354486i	0.984167	−	0.177243i	$-0.0567179\pi$
$230$	6.93622	−	6.03013i	0.457360	−	0.397615i
$231$		0			0
$232$	−2.29519	−	2.29519i	−0.150687	−	0.150687i
$233$	−8.10424	−	8.10424i	−0.530927	−	0.530927i	0.389921	−	0.920848i	$-0.372502\pi$
$233$	−8.10424	−	8.10424i	−0.530927	−	0.530927i	−0.920848	+	0.389921i	$0.872502\pi$
$234$		0			0
$235$	0.779481	−	11.1546i	0.0508477	−	0.727649i
$236$			6.33213i			0.412186i
$237$		0			0
$238$	−0.403777	+	0.403777i	−0.0261730	+	0.0261730i
$239$	−30.3794			−1.96508			−0.982541	−	0.186045i	$-0.940433\pi$
$239$	−30.3794			−1.96508			−0.982541	+	0.186045i	$0.940433\pi$
$240$		0			0
$241$	−14.6449			−0.943364			−0.471682	−	0.881769i	$-0.656353\pi$
$241$	−14.6449			−0.943364			−0.471682	+	0.881769i	$0.656353\pi$
$242$	−0.707107	+	0.707107i	−0.0454545	+	0.0454545i
$243$		0			0
$244$			1.69396i			0.108445i
$245$	10.1269	+	11.6486i	0.646985	+	0.744201i
$246$		0			0
$247$	−5.88517	−	5.88517i	−0.374464	−	0.374464i
$248$	−4.11032	−	4.11032i	−0.261005	−	0.261005i
$249$		0			0
$250$	10.9364	+	2.32298i	0.691676	+	0.146918i
$251$		−	5.75251i		−	0.363095i	−0.983382	−	0.181548i	$-0.941889\pi$
$251$		−	5.75251i		−	0.363095i	0.983382	−	0.181548i	$-0.0581106\pi$
$252$		0			0
$253$	−2.90643	+	2.90643i	−0.182726	+	0.182726i
$254$	−3.27983			−0.205795
$255$		0			0
$256$	1.00000			0.0625000
$257$	16.3846	−	16.3846i	1.02204	−	1.02204i	0.0222888	−	0.999752i	$-0.492905\pi$
$257$	16.3846	−	16.3846i	1.02204	−	1.02204i	0.999752	−	0.0222888i	$-0.00709533\pi$
$258$		0			0
$259$			3.20391i			0.199081i
$260$	11.2581	+	0.786709i	0.698196	+	0.0487896i
$261$		0			0
$262$	−1.82617	−	1.82617i	−0.112821	−	0.112821i
$263$	2.43637	+	2.43637i	0.150233	+	0.150233i	0.778222	−	0.627989i	$-0.216122\pi$
$263$	2.43637	+	2.43637i	0.150233	+	0.150233i	−0.627989	+	0.778222i	$0.716122\pi$
$264$		0			0
$265$	−19.0326	−	1.32999i	−1.16916	−	0.0817005i
$266$			0.514096i			0.0315212i
$267$		0			0
$268$	2.68599	−	2.68599i	0.164073	−	0.164073i
$269$	14.4426			0.880582			0.440291	−	0.897855i	$-0.354875\pi$
$269$	14.4426			0.880582			0.440291	+	0.897855i	$0.354875\pi$
$270$		0			0
$271$	−21.1249			−1.28324			−0.641622	−	0.767021i	$-0.721738\pi$
$271$	−21.1249			−1.28324			−0.641622	+	0.767021i	$0.721738\pi$
$272$	−1.29519	+	1.29519i	−0.0785327	+	0.0785327i
$273$		0			0
$274$			3.39080i			0.204846i
$275$	−4.95141	−	0.695400i	−0.298581	−	0.0419342i
$276$		0			0
$277$	11.5683	+	11.5683i	0.695070	+	0.695070i	0.963343	−	0.268273i	$-0.0864528\pi$
$277$	11.5683	+	11.5683i	0.695070	+	0.695070i	−0.268273	+	0.963343i	$0.586453\pi$
$278$	10.8229	+	10.8229i	0.649115	+	0.649115i
$279$		0			0
$280$	−0.457360	−	0.526083i	−0.0273325	−	0.0314395i
$281$			1.01801i			0.0607295i	0.999539	+	0.0303648i	$0.00966689\pi$
$281$			1.01801i			0.0607295i	−0.999539	+	0.0303648i	$0.990333\pi$
$282$		0			0
$283$	−19.3736	+	19.3736i	−1.15164	+	1.15164i	−0.165417	+	0.986224i	$0.552897\pi$
$283$	−19.3736	+	19.3736i	−1.15164	+	1.15164i	−0.986224	+	0.165417i	$0.947103\pi$
$284$	0.733819			0.0435442
$285$		0			0
$286$	−5.04704			−0.298438
$287$	−1.09633	+	1.09633i	−0.0647141	+	0.0647141i
$288$		0			0
$289$			13.6449i			0.802644i
$290$	−0.505955	+	7.24038i	−0.0297107	+	0.425170i
$291$		0			0
$292$	−2.84498	−	2.84498i	−0.166490	−	0.166490i
$293$	21.5194	+	21.5194i	1.25718	+	1.25718i	0.952436	+	0.304739i	$0.0985693\pi$
$293$	21.5194	+	21.5194i	1.25718	+	1.25718i	0.304739	+	0.952436i	$0.401431\pi$
$294$		0			0
$295$	10.6855	−	9.28968i	0.622136	−	0.540866i
$296$			10.2772i			0.597348i
$297$		0			0
$298$	5.73675	−	5.73675i	0.332321	−	0.332321i
$299$	−20.7450			−1.19971
$300$		0			0
$301$	−2.78746			−0.160667
$302$	−6.14415	+	6.14415i	−0.353556	+	0.353556i
$303$		0			0
$304$			1.64906i			0.0945802i
$305$	2.85858	−	2.48516i	0.163682	−	0.142300i
$306$		0			0
$307$	8.30937	+	8.30937i	0.474241	+	0.474241i	0.903284	−	0.429043i	$-0.141149\pi$
$307$	8.30937	+	8.30937i	0.474241	+	0.474241i	−0.429043	+	0.903284i	$0.641149\pi$
$308$	0.220441	+	0.220441i	0.0125608	+	0.0125608i
$309$		0			0
$310$	−0.906082	+	12.9663i	−0.0514620	+	0.736439i
$311$		−	7.84346i		−	0.444762i	−0.974960	−	0.222381i	$-0.928617\pi$
$311$		−	7.84346i		−	0.444762i	0.974960	−	0.222381i	$-0.0713829\pi$
$312$		0			0
$313$	11.5937	−	11.5937i	0.655313	−	0.655313i	−0.298955	−	0.954267i	$-0.596638\pi$
$313$	11.5937	−	11.5937i	0.655313	−	0.655313i	0.954267	+	0.298955i	$0.0966379\pi$
$314$	−16.3281			−0.921446
$315$		0			0
$316$	13.9310			0.783679
$317$	2.43344	−	2.43344i	0.136676	−	0.136676i	−0.635459	−	0.772135i	$-0.719189\pi$
$317$	2.43344	−	2.43344i	0.136676	−	0.136676i	0.772135	+	0.635459i	$0.219189\pi$
$318$		0			0
$319$		−	3.24589i		−	0.181735i
$320$	−1.46707	−	1.68751i	−0.0820118	−	0.0943348i
$321$		0			0
$322$	0.906082	+	0.906082i	0.0504940	+	0.0504940i
$323$	−2.13585	−	2.13585i	−0.118842	−	0.118842i
$324$		0			0
$325$	−15.1888	−	20.1523i	−0.842525	−	1.11785i
$326$			11.5913i			0.641981i
$327$		0			0
$328$	−3.51668	+	3.51668i	−0.194176	+	0.194176i
$329$	1.55896			0.0859484
$330$		0			0
$331$	−14.5295			−0.798615			−0.399307	−	0.916817i	$-0.630749\pi$
$331$	−14.5295			−0.798615			−0.399307	+	0.916817i	$0.630749\pi$
$332$	3.45193	−	3.45193i	0.189449	−	0.189449i
$333$		0			0
$334$		−	21.6192i		−	1.18295i
$335$	−8.47319	−	0.592103i	−0.462940	−	0.0323500i
$336$		0			0
$337$	−0.238212	−	0.238212i	−0.0129762	−	0.0129762i	0.700589	−	0.713565i	$-0.252921\pi$
$337$	−0.238212	−	0.238212i	−0.0129762	−	0.0129762i	−0.713565	+	0.700589i	$0.752921\pi$
$338$	−8.81949	−	8.81949i	−0.479717	−	0.479717i
$339$		0			0
$340$	4.08580	+	0.285514i	0.221584	+	0.0154842i
$341$		−	5.81287i		−	0.314784i
$342$		0			0
$343$	−3.06475	+	3.06475i	−0.165481	+	0.165481i
$344$	−8.94133			−0.482084
$345$		0			0
$346$	−0.453680			−0.0243900
$347$	6.13171	−	6.13171i	0.329168	−	0.329168i	−0.523102	−	0.852270i	$-0.675225\pi$
$347$	6.13171	−	6.13171i	0.329168	−	0.329168i	0.852270	+	0.523102i	$0.175225\pi$
$348$		0			0
$349$			31.0087i			1.65986i	0.557869	+	0.829929i	$0.311619\pi$
$349$			31.0087i			1.65986i	−0.557869	+	0.829929i	$0.688381\pi$
$350$	−0.216791	+	1.54360i	−0.0115880	+	0.0825091i
$351$		0			0
$352$	0.707107	+	0.707107i	0.0376889	+	0.0376889i
$353$	−22.6991	−	22.6991i	−1.20815	−	1.20815i	−0.971625	−	0.236528i	$-0.923991\pi$
$353$	−22.6991	−	22.6991i	−1.20815	−	1.20815i	−0.236528	−	0.971625i	$-0.576009\pi$
$354$		0			0
$355$	−1.07657	−	1.23833i	−0.0571382	−	0.0657237i
$356$			14.0326i			0.743724i
$357$		0			0
$358$	8.36665	−	8.36665i	0.442191	−	0.442191i
$359$	14.8579			0.784172			0.392086	−	0.919928i	$-0.371754\pi$
$359$	14.8579			0.784172			0.392086	+	0.919928i	$0.371754\pi$
$360$		0			0
$361$	16.2806			0.856873
$362$	2.01623	−	2.01623i	0.105971	−	0.105971i
$363$		0			0
$364$			1.57342i			0.0824695i
$365$	−0.627151	+	8.97474i	−0.0328266	+	0.469759i
$366$		0			0
$367$	12.5695	+	12.5695i	0.656123	+	0.656123i	0.954461	−	0.298337i	$-0.0964320\pi$
$367$	12.5695	+	12.5695i	0.656123	+	0.656123i	−0.298337	+	0.954461i	$0.596432\pi$
$368$	2.90643	+	2.90643i	0.151508	+	0.151508i
$369$		0			0
$370$	17.3428	−	15.0773i	0.901612	−	0.783834i
$371$		−	2.65998i		−	0.138099i
$372$		0			0
$373$	10.6478	−	10.6478i	0.551325	−	0.551325i	−0.375498	−	0.926823i	$-0.622528\pi$
$373$	10.6478	−	10.6478i	0.551325	−	0.551325i	0.926823	+	0.375498i	$0.122528\pi$
$374$	−1.83168			−0.0947140
$375$		0			0
$376$	5.00067			0.257890
$377$	11.5839	−	11.5839i	0.596603	−	0.596603i
$378$		0			0
$379$			28.4169i			1.45968i	0.683619	+	0.729839i	$0.260405\pi$
$379$			28.4169i			1.45968i	−0.683619	+	0.729839i	$0.739595\pi$
$380$	2.78281	−	2.41929i	0.142755	−	0.124107i
$381$		0			0
$382$	17.3259	+	17.3259i	0.886471	+	0.886471i
$383$	−3.82895	−	3.82895i	−0.195650	−	0.195650i	0.602482	−	0.798132i	$-0.294178\pi$
$383$	−3.82895	−	3.82895i	−0.195650	−	0.195650i	−0.798132	+	0.602482i	$0.794178\pi$
$384$		0			0
$385$	0.0485942	−	0.695400i	0.00247659	−	0.0354408i
$386$		−	14.1815i		−	0.721820i
$387$		0			0
$388$	4.93128	−	4.93128i	0.250348	−	0.250348i
$389$	10.0431			0.509203			0.254601	−	0.967046i	$-0.418056\pi$
$389$	10.0431			0.509203			0.254601	+	0.967046i	$0.418056\pi$
$390$		0			0
$391$	−7.52879			−0.380747
$392$	−4.88102	+	4.88102i	−0.246529	+	0.246529i
$393$		0			0
$394$		−	21.4936i		−	1.08283i
$395$	−20.4377	−	23.5087i	−1.02833	−	1.18285i
$396$		0			0
$397$	−12.1157	−	12.1157i	−0.608070	−	0.608070i	0.334372	−	0.942441i	$-0.391476\pi$
$397$	−12.1157	−	12.1157i	−0.608070	−	0.608070i	−0.942441	+	0.334372i	$0.891476\pi$
$398$	17.4676	+	17.4676i	0.875574	+	0.875574i
$399$		0			0
$400$	−0.695400	+	4.95141i	−0.0347700	+	0.247570i
$401$		−	37.2698i		−	1.86116i	−0.366083	−	0.930582i	$-0.619301\pi$
$401$		−	37.2698i		−	1.86116i	0.366083	−	0.930582i	$-0.380699\pi$
$402$		0			0
$403$	20.7450	−	20.7450i	1.03338	−	1.03338i
$404$	−7.22294			−0.359355
$405$		0			0
$406$	−1.01191			−0.0502202
$407$	−7.26705	+	7.26705i	−0.360214	+	0.360214i
$408$		0			0
$409$		−	2.55163i		−	0.126170i	−0.998008	−	0.0630851i	$-0.979906\pi$
$409$		−	2.55163i		−	0.126170i	0.998008	−	0.0630851i	$-0.0200939\pi$
$410$	11.0937	+	0.775219i	0.547877	+	0.0382854i
$411$		0			0
$412$	−13.0883	−	13.0883i	−0.644812	−	0.644812i
$413$	1.39586	+	1.39586i	0.0686858	+	0.0686858i
$414$		0			0
$415$	−10.8894	−	0.760946i	−0.534540	−	0.0373534i
$416$			5.04704i			0.247452i
$417$		0			0
$418$	−1.16606	+	1.16606i	−0.0570340	+	0.0570340i
$419$	−33.6631			−1.64455			−0.822275	−	0.569090i	$-0.807296\pi$
$419$	−33.6631			−1.64455			−0.822275	+	0.569090i	$0.807296\pi$
$420$		0			0
$421$	13.0333			0.635202			0.317601	−	0.948224i	$-0.397123\pi$
$421$	13.0333			0.635202			0.317601	+	0.948224i	$0.397123\pi$
$422$	3.20424	−	3.20424i	0.155980	−	0.155980i
$423$		0			0
$424$		−	8.53239i		−	0.414369i
$425$	−5.51235	−	7.31371i	−0.267388	−	0.354767i
$426$		0			0
$427$	0.373418	+	0.373418i	0.0180710	+	0.0180710i
$428$	6.08443	+	6.08443i	0.294102	+	0.294102i
$429$		0			0
$430$	13.1176	+	15.0886i	0.632585	+	0.727637i
$431$			0.991169i			0.0477429i	0.999715	+	0.0238715i	$0.00759924\pi$
$431$			0.991169i			0.0477429i	−0.999715	+	0.0238715i	$0.992401\pi$
$432$		0			0
$433$	12.9422	−	12.9422i	0.621963	−	0.621963i	−0.324070	−	0.946033i	$-0.605051\pi$
$433$	12.9422	−	12.9422i	0.621963	−	0.621963i	0.946033	+	0.324070i	$0.105051\pi$
$434$	−1.81216			−0.0869867
$435$		0			0
$436$	15.4240			0.738677
$437$	−4.79289	+	4.79289i	−0.229275	+	0.229275i
$438$		0			0
$439$			1.03879i			0.0495788i	0.999693	+	0.0247894i	$0.00789152\pi$
$439$			1.03879i			0.0495788i	−0.999693	+	0.0247894i	$0.992108\pi$
$440$	0.155875	−	2.23063i	0.00743106	−	0.106341i
$441$		0			0
$442$	−6.53690	−	6.53690i	−0.310929	−	0.310929i
$443$	18.8125	+	18.8125i	0.893810	+	0.893810i	0.994879	−	0.101069i	$-0.0322264\pi$
$443$	18.8125	+	18.8125i	0.893810	+	0.893810i	−0.101069	+	0.994879i	$0.532226\pi$
$444$		0			0
$445$	23.6801	−	20.5868i	1.12255	−	0.975906i
$446$			0.922513i			0.0436823i
$447$		0			0
$448$	0.220441	−	0.220441i	0.0104149	−	0.0104149i
$449$	7.45097			0.351633			0.175817	−	0.984423i	$-0.443743\pi$
$449$	7.45097			0.351633			0.175817	+	0.984423i	$0.443743\pi$
$450$		0			0
$451$	−4.97333			−0.234185
$452$	1.01545	−	1.01545i	0.0477627	−	0.0477627i
$453$		0			0
$454$		−	2.96342i		−	0.139080i
$455$	2.65516	−	2.30832i	0.124476	−	0.108216i
$456$		0			0
$457$	−24.7619	−	24.7619i	−1.15831	−	1.15831i	−0.984838	−	0.173477i	$-0.944500\pi$
$457$	−24.7619	−	24.7619i	−1.15831	−	1.15831i	−0.173477	−	0.984838i	$-0.555500\pi$
$458$	−3.79317	−	3.79317i	−0.177243	−	0.177243i
$459$		0			0
$460$	0.640697	−	9.16859i	0.0298726	−	0.427488i
$461$			37.0698i			1.72651i	0.504766	+	0.863256i	$0.331579\pi$
$461$			37.0698i			1.72651i	−0.504766	+	0.863256i	$0.668421\pi$
$462$		0			0
$463$	−19.4204	+	19.4204i	−0.902541	+	0.902541i	−0.995655	−	0.0931140i	$-0.970318\pi$
$463$	−19.4204	+	19.4204i	−0.902541	+	0.902541i	0.0931140	+	0.995655i	$0.470318\pi$
$464$	−3.24589			−0.150687
$465$		0			0
$466$	−11.4611			−0.530927
$467$	−0.949119	+	0.949119i	−0.0439200	+	0.0439200i	−0.728726	−	0.684806i	$-0.759887\pi$
$467$	−0.949119	+	0.949119i	−0.0439200	+	0.0439200i	0.684806	+	0.728726i	$0.259887\pi$
$468$		0			0
$469$		−	1.18421i		−	0.0546815i
$470$	−7.33635	−	8.43870i	−0.338400	−	0.389248i
$471$		0			0
$472$	4.47749	+	4.47749i	0.206093	+	0.206093i
$473$	−6.32247	−	6.32247i	−0.290708	−	0.290708i
$474$		0			0
$475$	−8.16517	−	1.14676i	−0.374644	−	0.0526168i
$476$			0.571027i			0.0261730i
$477$		0			0
$478$	−21.4815	+	21.4815i	−0.982541	+	0.982541i
$479$	−34.5759			−1.57981			−0.789907	−	0.613227i	$-0.789871\pi$
$479$	−34.5759			−1.57981			−0.789907	+	0.613227i	$0.789871\pi$
$480$		0			0
$481$	−51.8693			−2.36504
$482$	−10.3555	+	10.3555i	−0.471682	+	0.471682i
$483$		0			0
$484$			1.00000i			0.0454545i
$485$	−15.5561	−	1.08706i	−0.706368	−	0.0493606i
$486$		0			0
$487$	19.7458	+	19.7458i	0.894767	+	0.894767i	0.994967	−	0.100201i	$-0.0319485\pi$
$487$	19.7458	+	19.7458i	0.894767	+	0.894767i	−0.100201	+	0.994967i	$0.531948\pi$
$488$	1.19781	+	1.19781i	0.0542223	+	0.0542223i
$489$		0			0
$490$	15.3976	+	1.07598i	0.695593	+	0.0486077i
$491$		−	5.29573i		−	0.238993i	−0.992835	−	0.119497i	$-0.961872\pi$
$491$		−	5.29573i		−	0.238993i	0.992835	−	0.119497i	$-0.0381281\pi$
$492$		0			0
$493$	4.20406	−	4.20406i	0.189341	−	0.189341i
$494$	−8.32289			−0.374464
$495$		0			0
$496$	−5.81287			−0.261005
$497$	0.161764	−	0.161764i	0.00725610	−	0.00725610i
$498$		0			0
$499$		−	32.1794i		−	1.44055i	−0.693690	−	0.720274i	$-0.744016\pi$
$499$		−	32.1794i		−	1.44055i	0.693690	−	0.720274i	$-0.255984\pi$
$500$	9.37576	−	6.09057i	0.419297	−	0.272379i
$501$		0			0
$502$	−4.06764	−	4.06764i	−0.181548	−	0.181548i
$503$	−29.3990	−	29.3990i	−1.31084	−	1.31084i	−0.920799	−	0.390036i	$-0.872462\pi$
$503$	−29.3990	−	29.3990i	−1.31084	−	1.31084i	−0.390036	−	0.920799i	$-0.627538\pi$
$504$		0			0
$505$	10.5966	+	12.1888i	0.471541	+	0.542395i
$506$			4.11032i			0.182726i
$507$		0			0
$508$	−2.31919	+	2.31919i	−0.102897	+	0.102897i
$509$	14.0999			0.624968			0.312484	−	0.949923i	$-0.398839\pi$
$509$	14.0999			0.624968			0.312484	+	0.949923i	$0.398839\pi$
$510$		0			0
$511$	−1.25430			−0.0554870
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	23.1713i		−	1.02204i
$515$	−2.88519	+	41.2880i	−0.127136	+	1.81937i
$516$		0			0
$517$	3.53601	+	3.53601i	0.155514	+	0.155514i
$518$	2.26551	+	2.26551i	0.0995407	+	0.0995407i
$519$		0			0
$520$	8.51695	−	7.40438i	0.373493	−	0.324703i
$521$		−	30.2443i		−	1.32503i	−0.749050	−	0.662513i	$-0.769490\pi$
$521$		−	30.2443i		−	1.32503i	0.749050	−	0.662513i	$-0.230510\pi$
$522$		0			0
$523$	−2.57488	+	2.57488i	−0.112591	+	0.112591i	−0.761158	−	0.648567i	$-0.775369\pi$
$523$	−2.57488	+	2.57488i	−0.112591	+	0.112591i	0.648567	+	0.761158i	$0.275369\pi$
$524$	−2.58260			−0.112821
$525$		0			0
$526$	3.44555			0.150233
$527$	7.52879	−	7.52879i	0.327959	−	0.327959i
$528$		0			0
$529$		−	6.10528i		−	0.265447i
$530$	−14.3985	+	12.5176i	−0.625431	+	0.543731i
$531$		0			0
$532$	0.363521	+	0.363521i	0.0157606	+	0.0157606i
$533$	−17.7488	−	17.7488i	−0.768787	−	0.768787i
$534$		0			0
$535$	1.34126	−	19.1939i	0.0579876	−	0.829823i
$536$		−	3.79857i		−	0.164073i
$537$		0			0
$538$	10.2125	−	10.2125i	0.440291	−	0.440291i
$539$	−6.90281			−0.297325
$540$		0			0
$541$	31.5800			1.35773			0.678866	−	0.734262i	$-0.262472\pi$
$541$	31.5800			1.35773			0.678866	+	0.734262i	$0.262472\pi$
$542$	−14.9375	+	14.9375i	−0.641622	+	0.641622i
$543$		0			0
$544$			1.83168i			0.0785327i
$545$	−22.6282	−	26.0282i	−0.969284	−	1.11493i
$546$		0			0
$547$	22.3561	+	22.3561i	0.955879	+	0.955879i	0.999067	−	0.0431877i	$-0.0137514\pi$
$547$	22.3561	+	22.3561i	0.955879	+	0.955879i	−0.0431877	+	0.999067i	$0.513751\pi$
$548$	2.39766	+	2.39766i	0.102423	+	0.102423i
$549$		0			0
$550$	−3.99289	+	3.00945i	−0.170258	+	0.128323i
$551$		−	5.35268i		−	0.228032i
$552$		0			0
$553$	3.07096	−	3.07096i	0.130590	−	0.130590i
$554$	16.3600			0.695070
$555$		0			0
$556$	15.3059			0.649115
$557$	−12.3562	+	12.3562i	−0.523547	+	0.523547i	−0.918641	−	0.395094i	$-0.870712\pi$
$557$	−12.3562	+	12.3562i	−0.523547	+	0.523547i	0.395094	+	0.918641i	$0.370712\pi$
$558$		0			0
$559$		−	45.1273i		−	1.90868i
$560$	−0.695400	−	0.0485942i	−0.0293860	−	0.00205348i
$561$		0			0
$562$	0.719844	+	0.719844i	0.0303648	+	0.0303648i
$563$	−17.2529	−	17.2529i	−0.727123	−	0.727123i	0.242922	−	0.970046i	$-0.421894\pi$
$563$	−17.2529	−	17.2529i	−0.727123	−	0.727123i	−0.970046	+	0.242922i	$0.921894\pi$
$564$		0			0
$565$	−3.20332	−	0.223846i	−0.134765	−	0.00941729i
$566$			27.3984i			1.15164i
$567$		0			0
$568$	0.518889	−	0.518889i	0.0217721	−	0.0217721i
$569$	−11.4436			−0.479740			−0.239870	−	0.970805i	$-0.577105\pi$
$569$	−11.4436			−0.479740			−0.239870	+	0.970805i	$0.577105\pi$
$570$		0			0
$571$	−5.53623			−0.231684			−0.115842	−	0.993268i	$-0.536957\pi$
$571$	−5.53623			−0.231684			−0.115842	+	0.993268i	$0.536957\pi$
$572$	−3.56880	+	3.56880i	−0.149219	+	0.149219i
$573$		0			0
$574$			1.55044i			0.0647141i
$575$	−16.4121	+	12.3698i	−0.684431	+	0.515856i
$576$		0			0
$577$	10.9014	+	10.9014i	0.453833	+	0.453833i	0.896625	−	0.442792i	$-0.146012\pi$
$577$	10.9014	+	10.9014i	0.453833	+	0.453833i	−0.442792	+	0.896625i	$0.646012\pi$
$578$	9.64843	+	9.64843i	0.401322	+	0.401322i
$579$		0			0
$580$	4.76196	+	5.47749i	0.197730	+	0.227440i
$581$		−	1.52189i		−	0.0631387i
$582$		0			0
$583$	6.03331	−	6.03331i	0.249874	−	0.249874i
$584$	−4.02341			−0.166490
$585$		0			0
$586$	30.4330			1.25718
$587$	0.325923	−	0.325923i	0.0134523	−	0.0134523i	−0.700349	−	0.713801i	$-0.746972\pi$
$587$	0.325923	−	0.325923i	0.0134523	−	0.0134523i	0.713801	+	0.700349i	$0.246972\pi$
$588$		0			0
$589$		−	9.58578i		−	0.394975i
$590$	0.987022	−	14.1246i	0.0406350	−	0.581501i
$591$		0			0
$592$	7.26705	+	7.26705i	0.298674	+	0.298674i
$593$	−18.7609	−	18.7609i	−0.770416	−	0.770416i	0.207763	−	0.978179i	$-0.433382\pi$
$593$	−18.7609	−	18.7609i	−0.770416	−	0.770416i	−0.978179	+	0.207763i	$0.933382\pi$
$594$		0			0
$595$	0.963616	−	0.837738i	0.0395044	−	0.0343439i
$596$		−	8.11299i		−	0.332321i
$597$		0			0
$598$	−14.6689	+	14.6689i	−0.599856	+	0.599856i
$599$	6.62064			0.270512			0.135256	−	0.990811i	$-0.456814\pi$
$599$	6.62064			0.270512			0.135256	+	0.990811i	$0.456814\pi$
$600$		0			0
$601$	−32.0766			−1.30843			−0.654217	−	0.756307i	$-0.727002\pi$
$601$	−32.0766			−1.30843			−0.654217	+	0.756307i	$0.727002\pi$
$602$	−1.97103	+	1.97103i	−0.0803334	+	0.0803334i
$603$		0			0
$604$			8.68914i			0.353556i
$605$	1.68751	−	1.46707i	0.0686072	−	0.0596450i
$606$		0			0
$607$	15.0339	+	15.0339i	0.610208	+	0.610208i	0.943000	−	0.332792i	$-0.107991\pi$
$607$	15.0339	+	15.0339i	0.610208	+	0.610208i	−0.332792	+	0.943000i	$0.607991\pi$
$608$	1.16606	+	1.16606i	0.0472901	+	0.0472901i
$609$		0			0
$610$	0.264046	−	3.77859i	0.0106909	−	0.152991i
$611$			25.2386i			1.02104i
$612$		0			0
$613$	−8.10085	+	8.10085i	−0.327190	+	0.327190i	−0.851517	−	0.524327i	$-0.824317\pi$
$613$	−8.10085	+	8.10085i	−0.327190	+	0.327190i	0.524327	+	0.851517i	$0.324317\pi$
$614$	11.7512			0.474241
$615$		0			0
$616$	0.311751			0.0125608
$617$	22.1508	−	22.1508i	0.891756	−	0.891756i	−0.102932	−	0.994688i	$-0.532822\pi$
$617$	22.1508	−	22.1508i	0.891756	−	0.891756i	0.994688	+	0.102932i	$0.0328224\pi$
$618$		0			0
$619$		−	13.6051i		−	0.546834i	−0.961896	−	0.273417i	$-0.911846\pi$
$619$		−	13.6051i		−	0.546834i	0.961896	−	0.273417i	$-0.0881540\pi$
$620$	8.52790	+	9.80929i	0.342489	+	0.393951i
$621$		0			0
$622$	−5.54617	−	5.54617i	−0.222381	−	0.222381i
$623$	3.09335	+	3.09335i	0.123932	+	0.123932i
$624$		0			0
$625$	−24.0328	−	6.88641i	−0.961314	−	0.275456i
$626$		−	16.3959i		−	0.655313i
$627$		0			0
$628$	−11.5457	+	11.5457i	−0.460723	+	0.460723i
$629$	−18.8245			−0.750581
$630$		0			0
$631$	41.3096			1.64451			0.822254	−	0.569120i	$-0.192716\pi$
$631$	41.3096			1.64451			0.822254	+	0.569120i	$0.192716\pi$
$632$	9.85069	−	9.85069i	0.391839	−	0.391839i
$633$		0			0
$634$		−	3.44141i		−	0.136676i
$635$	7.31609	+	0.511245i	0.290330	+	0.0202881i
$636$		0			0
$637$	−24.6347	−	24.6347i	−0.976064	−	0.976064i
$638$	−2.29519	−	2.29519i	−0.0908676	−	0.0908676i
$639$		0			0
$640$	−2.23063	−	0.155875i	−0.0881733	−	0.00616151i
$641$			34.8513i			1.37654i	0.725453	+	0.688272i	$0.241630\pi$
$641$			34.8513i			1.37654i	−0.725453	+	0.688272i	$0.758370\pi$
$642$		0			0
$643$	12.9785	−	12.9785i	0.511822	−	0.511822i	−0.403262	−	0.915084i	$-0.632124\pi$
$643$	12.9785	−	12.9785i	0.511822	−	0.511822i	0.915084	+	0.403262i	$0.132124\pi$
$644$	1.28139			0.0504940
$645$		0			0
$646$	−3.02055			−0.118842
$647$	27.0946	−	27.0946i	1.06520	−	1.06520i	0.0674782	−	0.997721i	$-0.478505\pi$
$647$	27.0946	−	27.0946i	1.06520	−	1.06520i	0.997721	−	0.0674782i	$-0.0214953\pi$
$648$		0			0
$649$			6.33213i			0.248558i
$650$	−24.9900	−	3.50971i	−0.980187	−	0.137662i
$651$		0			0
$652$	8.19627	+	8.19627i	0.320991	+	0.320991i
$653$	34.5899	+	34.5899i	1.35361	+	1.35361i	0.881590	+	0.472017i	$0.156474\pi$
$653$	34.5899	+	34.5899i	1.35361	+	1.35361i	0.472017	+	0.881590i	$0.343526\pi$
$654$		0			0
$655$	3.78885	+	4.35816i	0.148043	+	0.170288i
$656$			4.97333i			0.194176i
$657$		0			0
$658$	1.10235	−	1.10235i	0.0429742	−	0.0429742i
$659$	15.8413			0.617088			0.308544	−	0.951210i	$-0.400158\pi$
$659$	15.8413			0.617088			0.308544	+	0.951210i	$0.400158\pi$
$660$		0			0
$661$	24.7558			0.962888			0.481444	−	0.876477i	$-0.340112\pi$
$661$	24.7558			0.962888			0.481444	+	0.876477i	$0.340112\pi$
$662$	−10.2739	+	10.2739i	−0.399307	+	0.399307i
$663$		0			0
$664$		−	4.88176i		−	0.189449i
$665$	0.0801348	−	1.14676i	0.00310750	−	0.0444693i
$666$		0			0
$667$	−9.43398	−	9.43398i	−0.365285	−	0.365285i
$668$	−15.2871	−	15.2871i	−0.591476	−	0.591476i
$669$		0			0
$670$	−6.41013	+	5.57277i	−0.247645	+	0.215295i
$671$			1.69396i			0.0653945i
$672$		0			0
$673$	1.61094	−	1.61094i	0.0620970	−	0.0620970i	−0.675376	−	0.737473i	$-0.736019\pi$
$673$	1.61094	−	1.61094i	0.0620970	−	0.0620970i	0.737473	+	0.675376i	$0.236019\pi$
$674$	−0.336883			−0.0129762
$675$		0			0
$676$	−12.4726			−0.479717
$677$	−16.3466	+	16.3466i	−0.628252	+	0.628252i	−0.947628	−	0.319376i	$-0.896527\pi$
$677$	−16.3466	+	16.3466i	−0.628252	+	0.628252i	0.319376	+	0.947628i	$0.396527\pi$
$678$		0			0
$679$		−	2.17411i		−	0.0834347i
$680$	3.09099	−	2.68721i	0.118534	−	0.103050i
$681$		0			0
$682$	−4.11032	−	4.11032i	−0.157392	−	0.157392i
$683$	5.57698	+	5.57698i	0.213397	+	0.213397i	0.805709	−	0.592312i	$-0.201785\pi$
$683$	5.57698	+	5.57698i	0.213397	+	0.213397i	−0.592312	+	0.805709i	$0.701785\pi$
$684$		0			0
$685$	0.528542	−	7.56361i	0.0201945	−	0.288991i
$686$			4.33421i			0.165481i
$687$		0			0
$688$	−6.32247	+	6.32247i	−0.241042	+	0.241042i
$689$	43.0633			1.64058
$690$		0			0
$691$	−28.1217			−1.06980			−0.534899	−	0.844916i	$-0.679650\pi$
$691$	−28.1217			−1.06980			−0.534899	+	0.844916i	$0.679650\pi$
$692$	−0.320800	+	0.320800i	−0.0121950	+	0.0121950i
$693$		0			0
$694$		−	8.67155i		−	0.329168i
$695$	−22.4549	−	25.8289i	−0.851762	−	0.979747i
$696$		0			0
$697$	−6.44143	−	6.44143i	−0.243987	−	0.243987i
$698$	21.9265	+	21.9265i	0.829929	+	0.829929i
$699$		0			0
$700$	0.938198	+	1.24479i	0.0354605	+	0.0470485i
$701$		−	13.6485i		−	0.515497i	−0.966212	−	0.257749i	$-0.917019\pi$
$701$		−	13.6485i		−	0.515497i	0.966212	−	0.257749i	$-0.0829806\pi$
$702$		0			0
$703$	−11.9838	+	11.9838i	−0.451978	+	0.451978i
$704$	1.00000			0.0376889
$705$		0			0
$706$	−32.1014			−1.20815
$707$	−1.59223	+	1.59223i	−0.0598820	+	0.0598820i
$708$		0			0
$709$			24.0511i			0.903259i	0.892206	+	0.451629i	$0.149157\pi$
$709$			24.0511i			0.903259i	−0.892206	+	0.451629i	$0.850843\pi$
$710$	−1.63688	−	0.114384i	−0.0614310	−	0.00429277i
$711$		0			0
$712$	9.92251	+	9.92251i	0.371862	+	0.371862i
$713$	−16.8947	−	16.8947i	−0.632712	−	0.632712i
$714$		0			0
$715$	11.2581	+	0.786709i	0.421028	+	0.0294213i
$716$		−	11.8322i		−	0.442191i
$717$		0			0
$718$	10.5062	−	10.5062i	0.392086	−	0.392086i
$719$	16.6685			0.621629			0.310814	−	0.950471i	$-0.399398\pi$
$719$	16.6685			0.621629			0.310814	+	0.950471i	$0.399398\pi$
$720$		0			0
$721$	−5.77037			−0.214900
$722$	11.5121	−	11.5121i	0.428437	−	0.428437i
$723$		0			0
$724$		−	2.85138i		−	0.105971i
$725$	2.25719	−	16.0717i	0.0838301	−	0.596889i
$726$		0			0
$727$	15.0266	+	15.0266i	0.557307	+	0.557307i	0.928540	−	0.371233i	$-0.121065\pi$
$727$	15.0266	+	15.0266i	0.557307	+	0.557307i	−0.371233	+	0.928540i	$0.621065\pi$
$728$	1.11257	+	1.11257i	0.0412348	+	0.0412348i
$729$		0			0
$730$	5.90264	+	6.78956i	0.218466	+	0.251293i
$731$		−	16.3777i		−	0.605750i
$732$		0			0
$733$	23.4209	−	23.4209i	0.865069	−	0.865069i	−0.126853	−	0.991922i	$-0.540488\pi$
$733$	23.4209	−	23.4209i	0.865069	−	0.865069i	0.991922	+	0.126853i	$0.0404875\pi$
$734$	17.7760			0.656123
$735$		0			0
$736$	4.11032			0.151508
$737$	2.68599	−	2.68599i	0.0989398	−	0.0989398i
$738$		0			0
$739$		−	9.10321i		−	0.334867i	−0.985883	−	0.167433i	$-0.946452\pi$
$739$		−	9.10321i		−	0.334867i	0.985883	−	0.167433i	$-0.0535479\pi$
$740$	1.60196	−	22.9245i	0.0588891	−	0.842723i
$741$		0			0
$742$	−1.88089	−	1.88089i	−0.0690495	−	0.0690495i
$743$	33.1249	+	33.1249i	1.21523	+	1.21523i	0.969282	+	0.245951i	$0.0791002\pi$
$743$	33.1249	+	33.1249i	1.21523	+	1.21523i	0.245951	+	0.969282i	$0.420900\pi$
$744$		0			0
$745$	−13.6908	+	11.9023i	−0.501591	+	0.436068i
$746$		−	15.0583i		−	0.551325i
$747$		0			0
$748$	−1.29519	+	1.29519i	−0.0473570	+	0.0473570i
$749$	2.68252			0.0980170
$750$		0			0
$751$	−36.0619			−1.31592			−0.657958	−	0.753055i	$-0.728580\pi$
$751$	−36.0619			−1.31592			−0.657958	+	0.753055i	$0.728580\pi$
$752$	3.53601	−	3.53601i	0.128945	−	0.128945i
$753$		0			0
$754$		−	16.3822i		−	0.596603i
$755$	14.6630	−	12.7476i	0.533642	−	0.463932i
$756$		0			0
$757$	27.8654	+	27.8654i	1.01278	+	1.01278i	0.999917	+	0.0128674i	$0.00409592\pi$
$757$	27.8654	+	27.8654i	1.01278	+	1.01278i	0.0128674	+	0.999917i	$0.495904\pi$
$758$	20.0938	+	20.0938i	0.729839	+	0.729839i
$759$		0			0
$760$	0.257048	−	3.67844i	0.00932411	−	0.133431i
$761$			1.06484i			0.0386005i	0.999814	+	0.0193002i	$0.00614384\pi$
$761$			1.06484i			0.0386005i	−0.999814	+	0.0193002i	$0.993856\pi$
$762$		0			0
$763$	3.40009	−	3.40009i	0.123091	−	0.123091i
$764$	24.5026			0.886471
$765$		0			0
$766$	−5.41495			−0.195650
$767$	−22.5981	+	22.5981i	−0.815969	+	0.815969i
$768$		0			0
$769$		−	16.1547i		−	0.582554i	−0.956639	−	0.291277i	$-0.905920\pi$
$769$		−	16.1547i		−	0.582554i	0.956639	−	0.291277i	$-0.0940801\pi$
$770$	−0.457360	−	0.526083i	−0.0164821	−	0.0189587i
$771$		0			0
$772$	−10.0278	−	10.0278i	−0.360910	−	0.360910i
$773$	6.90233	+	6.90233i	0.248260	+	0.248260i	0.820256	−	0.571996i	$-0.193831\pi$
$773$	6.90233	+	6.90233i	0.248260	+	0.248260i	−0.571996	+	0.820256i	$0.693831\pi$
$774$		0			0
$775$	4.04227	−	28.7819i	0.145202	−	1.03388i
$776$		−	6.97388i		−	0.250348i
$777$		0			0
$778$	7.10151	−	7.10151i	0.254601	−	0.254601i
$779$	−8.20133			−0.293843
$780$		0			0
$781$	0.733819			0.0262581
$782$	−5.32366	+	5.32366i	−0.190374	+	0.190374i
$783$		0			0
$784$			6.90281i			0.246529i
$785$	36.4219	+	2.54514i	1.29995	+	0.0908400i
$786$		0			0
$787$	31.9673	+	31.9673i	1.13951	+	1.13951i	0.988538	+	0.150972i	$0.0482403\pi$
$787$	31.9673	+	31.9673i	1.13951	+	1.13951i	0.150972	+	0.988538i	$0.451760\pi$
$788$	−15.1983	−	15.1983i	−0.541416	−	0.541416i
$789$		0			0
$790$	−31.0748	−	2.17150i	−1.10559	−	0.0772583i
$791$		−	0.447693i		−	0.0159181i
$792$		0			0
$793$	−6.04540	+	6.04540i	−0.214678	+	0.214678i
$794$	−17.1342			−0.608070
$795$		0			0
$796$	24.7030			0.875574
$797$	−10.6223	+	10.6223i	−0.376262	+	0.376262i	−0.869752	−	0.493490i	$-0.835721\pi$
$797$	−10.6223	+	10.6223i	−0.376262	+	0.376262i	0.493490	+	0.869752i	$0.335721\pi$
$798$		0			0
$799$			9.15964i			0.324045i
$800$	3.00945	+	3.99289i	0.106400	+	0.141170i
$801$		0			0
$802$	−26.3537	−	26.3537i	−0.930582	−	0.930582i
$803$	−2.84498	−	2.84498i	−0.100397	−	0.100397i
$804$		0			0
$805$	−1.87990	−	2.16237i	−0.0662577	−	0.0762135i
$806$		−	29.3378i		−	1.03338i
$807$		0			0
$808$	−5.10739	+	5.10739i	−0.179677	+	0.179677i
$809$	55.8710			1.96432			0.982160	−	0.188049i	$-0.0602165\pi$
$809$	55.8710			1.96432			0.982160	+	0.188049i	$0.0602165\pi$
$810$		0			0
$811$	−13.1843			−0.462964			−0.231482	−	0.972839i	$-0.574357\pi$
$811$	−13.1843			−0.462964			−0.231482	+	0.972839i	$0.574357\pi$
$812$	−0.715528	+	0.715528i	−0.0251101	+	0.0251101i
$813$		0			0
$814$			10.2772i			0.360214i
$815$	1.80679	−	25.8558i	0.0632892	−	0.905690i
$816$		0			0
$817$	−10.4261	−	10.4261i	−0.364765	−	0.364765i
$818$	−1.80428	−	1.80428i	−0.0630851	−	0.0630851i
$819$		0			0
$820$	8.39256	−	7.29624i	0.293081	−	0.254796i
$821$			31.8795i			1.11260i	0.830981	+	0.556301i	$0.187780\pi$
$821$			31.8795i			1.11260i	−0.830981	+	0.556301i	$0.812220\pi$
$822$		0			0
$823$	7.18547	−	7.18547i	0.250470	−	0.250470i	−0.570694	−	0.821163i	$-0.693326\pi$
$823$	7.18547	−	7.18547i	0.250470	−	0.250470i	0.821163	+	0.570694i	$0.193326\pi$
$824$	−18.5096			−0.644812
$825$		0			0
$826$	1.97404			0.0686858
$827$	18.7986	−	18.7986i	0.653691	−	0.653691i	−0.300189	−	0.953880i	$-0.597050\pi$
$827$	18.7986	−	18.7986i	0.653691	−	0.653691i	0.953880	+	0.300189i	$0.0970496\pi$
$828$		0			0
$829$		−	11.6858i		−	0.405865i	−0.979193	−	0.202932i	$-0.934953\pi$
$829$		−	11.6858i		−	0.405865i	0.979193	−	0.202932i	$-0.0650471\pi$
$830$	−8.23804	+	7.16190i	−0.285947	+	0.248593i
$831$		0			0
$832$	3.56880	+	3.56880i	0.123726	+	0.123726i
$833$	−8.94048	−	8.94048i	−0.309769	−	0.309769i
$834$		0			0
$835$	−3.36990	+	48.2245i	−0.116620	+	1.66888i
$836$			1.64906i			0.0570340i
$837$		0			0
$838$	−23.8034	+	23.8034i	−0.822275	+	0.822275i
$839$	45.6504			1.57603			0.788014	−	0.615657i	$-0.211109\pi$
$839$	45.6504			1.57603			0.788014	+	0.615657i	$0.211109\pi$
$840$		0			0
$841$	−18.4642			−0.636695
$842$	9.21591	−	9.21591i	0.317601	−	0.317601i
$843$		0			0
$844$		−	4.53147i		−	0.155980i
$845$	18.2983	+	21.0477i	0.629480	+	0.724065i
$846$		0			0
$847$	0.220441	+	0.220441i	0.00757444	+	0.00757444i
$848$	−6.03331	−	6.03331i	−0.207185	−	0.207185i
$849$		0			0
$850$	−9.06940	−	1.27375i	−0.311078	−	0.0436893i
$851$			42.2424i			1.44805i
$852$		0			0
$853$	−26.3300	+	26.3300i	−0.901524	+	0.901524i	−0.995568	−	0.0940443i	$-0.970020\pi$
$853$	−26.3300	+	26.3300i	−0.901524	+	0.901524i	0.0940443	+	0.995568i	$0.470020\pi$
$854$	0.528092			0.0180710
$855$		0			0
$856$	8.60469			0.294102
$857$	−18.3854	+	18.3854i	−0.628033	+	0.628033i	−0.947573	−	0.319540i	$-0.896472\pi$
$857$	−18.3854	+	18.3854i	−0.628033	+	0.628033i	0.319540	+	0.947573i	$0.396472\pi$
$858$		0			0
$859$		−	5.40669i		−	0.184474i	−0.995737	−	0.0922369i	$-0.970598\pi$
$859$		−	5.40669i		−	0.184474i	0.995737	−	0.0922369i	$-0.0294017\pi$
$860$	19.9448	+	1.39373i	0.680111	+	0.0475259i
$861$		0			0
$862$	0.700862	+	0.700862i	0.0238715	+	0.0238715i
$863$	−5.50836	−	5.50836i	−0.187507	−	0.187507i	0.607111	−	0.794617i	$-0.292329\pi$
$863$	−5.50836	−	5.50836i	−0.187507	−	0.187507i	−0.794617	+	0.607111i	$0.792329\pi$
$864$		0			0
$865$	1.01199	+	0.0707175i	0.0344088	+	0.00240447i
$866$		−	18.3031i		−	0.621963i
$867$		0			0
$868$	−1.28139	+	1.28139i	−0.0434933	+	0.0434933i
$869$	13.9310			0.472576
$870$		0			0
$871$	19.1715			0.649603
$872$	10.9064	−	10.9064i	0.369338	−	0.369338i
$873$		0			0
$874$			6.77817i			0.229275i
$875$	0.724190	−	3.40941i	0.0244821	−	0.115259i
$876$		0			0
$877$	12.1862	+	12.1862i	0.411500	+	0.411500i	0.882261	−	0.470761i	$-0.156021\pi$
$877$	12.1862	+	12.1862i	0.411500	+	0.411500i	−0.470761	+	0.882261i	$0.656021\pi$
$878$	0.734537	+	0.734537i	0.0247894	+	0.0247894i
$879$		0			0
$880$	−1.46707	−	1.68751i	−0.0494550	−	0.0568860i
$881$			15.9794i			0.538361i	0.963090	+	0.269180i	$0.0867528\pi$
$881$			15.9794i			0.538361i	−0.963090	+	0.269180i	$0.913247\pi$
$882$		0			0
$883$	−8.49960	+	8.49960i	−0.286034	+	0.286034i	−0.835510	−	0.549476i	$-0.814828\pi$
$883$	−8.49960	+	8.49960i	−0.286034	+	0.286034i	0.549476	+	0.835510i	$0.314828\pi$
$884$	−9.24457			−0.310929
$885$		0			0
$886$	26.6049			0.893810
$887$	−29.4073	+	29.4073i	−0.987400	+	0.987400i	−0.999922	−	0.0125212i	$-0.996014\pi$
$887$	−29.4073	+	29.4073i	−0.987400	+	0.987400i	0.0125212	+	0.999922i	$0.496014\pi$
$888$		0			0
$889$			1.02249i			0.0342932i
$890$	2.18733	−	31.3014i	0.0733194	−	1.04923i
$891$		0			0
$892$	0.652316	+	0.652316i	0.0218411	+	0.0218411i
$893$	5.83110	+	5.83110i	0.195130	+	0.195130i
$894$		0			0
$895$	−19.9670	+	17.3587i	−0.667424	+	0.580238i
$896$		−	0.311751i		−	0.0104149i
$897$		0			0
$898$	5.26863	−	5.26863i	0.175817	−	0.175817i
$899$	18.8680			0.629282
$900$		0			0
$901$	15.6286			0.520665
$902$	−3.51668	+	3.51668i	−0.117093	+	0.117093i
$903$		0			0
$904$		−	1.43606i		−	0.0477627i
$905$	−4.81175	+	4.18318i	−0.159948	+	0.139054i
$906$		0			0
$907$	16.3267	+	16.3267i	0.542118	+	0.542118i	0.924149	−	0.382031i	$-0.124775\pi$
$907$	16.3267	+	16.3267i	0.542118	+	0.542118i	−0.382031	+	0.924149i	$0.624775\pi$
$908$	−2.09545	−	2.09545i	−0.0695401	−	0.0695401i
$909$		0			0
$910$	0.245257	−	3.50971i	0.00813019	−	0.116346i
$911$		−	13.7949i		−	0.457046i	−0.973539	−	0.228523i	$-0.926610\pi$
$911$		−	13.7949i		−	0.457046i	0.973539	−	0.228523i	$-0.0733896\pi$
$912$		0			0
$913$	3.45193	−	3.45193i	0.114242	−	0.114242i
$914$	−35.0187			−1.15831
$915$		0			0
$916$	−5.36435			−0.177243
$917$	−0.569310	+	0.569310i	−0.0188003	+	0.0188003i
$918$		0			0
$919$			47.3513i			1.56197i	0.624547	+	0.780987i	$0.285284\pi$
$919$			47.3513i			1.56197i	−0.624547	+	0.780987i	$0.714716\pi$
$920$	−6.03013	−	6.93622i	−0.198808	−	0.228680i
$921$		0			0
$922$	26.2123	+	26.2123i	0.863256	+	0.863256i
$923$	2.61885	+	2.61885i	0.0862006	+	0.0862006i
$924$		0			0
$925$	−41.0356	+	30.9286i	−1.34924	+	1.01693i
$926$			27.4646i			0.902541i
$927$		0			0
$928$	−2.29519	+	2.29519i	−0.0753434	+	0.0753434i
$929$	32.1504			1.05482			0.527411	−	0.849611i	$-0.323163\pi$
$929$	32.1504			1.05482			0.527411	+	0.849611i	$0.323163\pi$
$930$		0			0
$931$	−11.3832			−0.373068
$932$	−8.10424	+	8.10424i	−0.265463	+	0.265463i
$933$		0			0
$934$			1.34226i			0.0439200i
$935$	4.08580	+	0.285514i	0.133620	+	0.00933730i
$936$		0			0
$937$	−12.8869	−	12.8869i	−0.420998	−	0.420998i	0.464550	−	0.885547i	$-0.346216\pi$
$937$	−12.8869	−	12.8869i	−0.420998	−	0.420998i	−0.885547	+	0.464550i	$0.846216\pi$
$938$	−0.837360	−	0.837360i	−0.0273408	−	0.0273408i
$939$		0			0
$940$	−11.1546	−	0.779481i	−0.363824	−	0.0254239i
$941$			20.4404i			0.666339i	0.942867	+	0.333169i	$0.108118\pi$
$941$			20.4404i			0.666339i	−0.942867	+	0.333169i	$0.891882\pi$
$942$		0			0
$943$	−14.4547	+	14.4547i	−0.470709	+	0.470709i
$944$	6.33213			0.206093
$945$		0			0
$946$	−8.94133			−0.290708
$947$	1.98640	−	1.98640i	0.0645494	−	0.0645494i	−0.674095	−	0.738645i	$-0.735466\pi$
$947$	1.98640	−	1.98640i	0.0645494	−	0.0645494i	0.738645	+	0.674095i	$0.235466\pi$
$948$		0			0
$949$		−	20.3063i		−	0.659172i
$950$	−6.58453	+	4.96277i	−0.213630	+	0.161014i
$951$		0			0
$952$	0.403777	+	0.403777i	0.0130865	+	0.0130865i
$953$	1.04603	+	1.04603i	0.0338842	+	0.0338842i	0.723846	−	0.689962i	$-0.242373\pi$
$953$	1.04603	+	1.04603i	0.0338842	+	0.0338842i	−0.689962	+	0.723846i	$0.742373\pi$
$954$		0			0
$955$	−35.9470	−	41.3484i	−1.16322	−	1.33800i
$956$			30.3794i			0.982541i
$957$		0			0
$958$	−24.4489	+	24.4489i	−0.789907	+	0.789907i
$959$	1.05708			0.0341350
$960$		0			0
$961$	2.78944			0.0899818
$962$	−36.6771	+	36.6771i	−1.18252	+	1.18252i
$963$		0			0
$964$			14.6449i			0.471682i
$965$	−2.21055	+	31.6337i	−0.0711600	+	1.01832i
$966$		0			0
$967$	−14.6161	−	14.6161i	−0.470021	−	0.470021i	0.431900	−	0.901921i	$-0.357843\pi$
$967$	−14.6161	−	14.6161i	−0.470021	−	0.470021i	−0.901921	+	0.431900i	$0.857843\pi$
$968$	0.707107	+	0.707107i	0.0227273	+	0.0227273i
$969$		0			0
$970$	−11.7685	+	10.2312i	−0.377864	+	0.328503i
$971$			46.6249i			1.49627i	0.663549	+	0.748133i	$0.269049\pi$
$971$			46.6249i			1.49627i	−0.663549	+	0.748133i	$0.730951\pi$
$972$		0			0
$973$	3.37405	−	3.37405i	0.108167	−	0.108167i
$974$	27.9247			0.894767
$975$		0			0
$976$	1.69396			0.0542223
$977$	−23.2968	+	23.2968i	−0.745329	+	0.745329i	−0.973598	−	0.228269i	$-0.926693\pi$
$977$	−23.2968	+	23.2968i	−0.745329	+	0.745329i	0.228269	+	0.973598i	$0.426693\pi$
$978$		0			0
$979$			14.0326i			0.448482i
$980$	11.6486	−	10.1269i	0.372100	−	0.323493i
$981$		0			0
$982$	−3.74465	−	3.74465i	−0.119497	−	0.119497i
$983$	8.97262	+	8.97262i	0.286182	+	0.286182i	0.835568	−	0.549386i	$-0.185138\pi$
$983$	8.97262	+	8.97262i	0.286182	+	0.286182i	−0.549386	+	0.835568i	$0.685138\pi$
$984$		0			0
$985$	−3.35032	+	47.9442i	−0.106750	+	1.52763i
$986$		−	5.94544i		−	0.189341i
$987$		0			0
$988$	−5.88517	+	5.88517i	−0.187232	+	0.187232i
$989$	−36.7517			−1.16864
$990$		0			0
$991$	55.8361			1.77369			0.886845	−	0.462066i	$-0.152892\pi$
$991$	55.8361			1.77369			0.886845	+	0.462066i	$0.152892\pi$
$992$	−4.11032	+	4.11032i	−0.130503	+	0.130503i
$993$		0			0
$994$		−	0.228769i		−	0.00725610i
$995$	−36.2410	−	41.6866i	−1.14892	−	1.32155i
$996$		0			0
$997$	−20.1162	−	20.1162i	−0.637087	−	0.637087i	0.312749	−	0.949836i	$-0.398750\pi$
$997$	−20.1162	−	20.1162i	−0.637087	−	0.637087i	−0.949836	+	0.312749i	$0.898750\pi$
$998$	−22.7543	−	22.7543i	−0.720274	−	0.720274i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.k.c.287.4	✓	12
3.2	odd	2		990.2.k.d.287.3	yes	12
5.3	odd	4		990.2.k.d.683.3	yes	12
15.8	even	4	inner	990.2.k.c.683.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.k.c.287.4	✓	12	1.1	even	1	trivial
990.2.k.c.683.4	yes	12	15.8	even	4	inner
990.2.k.d.287.3	yes	12	3.2	odd	2
990.2.k.d.683.3	yes	12	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.68751 + 1.46707i) q^{5} +(-0.220441 - 0.220441i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.155875 + 2.23063i) q^{10} -1.00000i q^{11} +(3.56880 - 3.56880i) q^{13} -0.311751 q^{14} -1.00000 q^{16} +(1.29519 - 1.29519i) q^{17} -1.64906i q^{19} +(1.46707 + 1.68751i) q^{20} +(-0.707107 - 0.707107i) q^{22} +(-2.90643 - 2.90643i) q^{23} +(0.695400 - 4.95141i) q^{25} -5.04704i q^{26} +(-0.220441 + 0.220441i) q^{28} +3.24589 q^{29} +5.81287 q^{31} +(-0.707107 + 0.707107i) q^{32} -1.83168i q^{34} +(0.695400 + 0.0485942i) q^{35} +(-7.26705 - 7.26705i) q^{37} +(-1.16606 - 1.16606i) q^{38} +(2.23063 + 0.155875i) q^{40} -4.97333i q^{41} +(6.32247 - 6.32247i) q^{43} -1.00000 q^{44} -4.11032 q^{46} +(-3.53601 + 3.53601i) q^{47} -6.90281i q^{49} +(-3.00945 - 3.99289i) q^{50} +(-3.56880 - 3.56880i) q^{52} +(6.03331 + 6.03331i) q^{53} +(1.46707 + 1.68751i) q^{55} +0.311751i q^{56} +(2.29519 - 2.29519i) q^{58} -6.33213 q^{59} -1.69396 q^{61} +(4.11032 - 4.11032i) q^{62} +1.00000i q^{64} +(-0.786709 + 11.2581i) q^{65} +(2.68599 + 2.68599i) q^{67} +(-1.29519 - 1.29519i) q^{68} +(0.526083 - 0.457360i) q^{70} +0.733819i q^{71} +(2.84498 - 2.84498i) q^{73} -10.2772 q^{74} -1.64906 q^{76} +(-0.220441 + 0.220441i) q^{77} +13.9310i q^{79} +(1.68751 - 1.46707i) q^{80} +(-3.51668 - 3.51668i) q^{82} +(3.45193 + 3.45193i) q^{83} +(-0.285514 + 4.08580i) q^{85} -8.94133i q^{86} +(-0.707107 + 0.707107i) q^{88} -14.0326 q^{89} -1.57342 q^{91} +(-2.90643 + 2.90643i) q^{92} +5.00067i q^{94} +(2.41929 + 2.78281i) q^{95} +(4.93128 + 4.93128i) q^{97} +(-4.88102 - 4.88102i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{13} - 12 q^{16} - 8 q^{17} + 8 q^{23} - 16 q^{31} - 4 q^{37} + 8 q^{38} + 4 q^{40} + 8 q^{43} - 12 q^{44} + 16 q^{46} + 24 q^{47} + 8 q^{50} + 12 q^{52} - 16 q^{53} + 4 q^{58} - 32 q^{59} + 16 q^{61}+ \cdots + 24 q^{98}+O(q^{100}) \) 12 * q - 12 * q^13 - 12 * q^16 - 8 * q^17 + 8 * q^23 - 16 * q^31 - 4 * q^37 + 8 * q^38 + 4 * q^40 + 8 * q^43 - 12 * q^44 + 16 * q^46 + 24 * q^47 + 8 * q^50 + 12 * q^52 - 16 * q^53 + 4 * q^58 - 32 * q^59 + 16 * q^61 - 16 * q^62 - 8 * q^67 + 8 * q^68 + 8 * q^70 + 20 * q^73 - 32 * q^74 - 12 * q^82 - 40 * q^85 + 8 * q^92 + 16 * q^95 + 36 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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